The knowledge of the absolute masses of neutrinos is still lacking despite
the precise determination of mass squared differences from neutrino oscillation experiments[1]}, [2]}, [3]}, [4]}.
If the neutrino mass type is Majorana, the lightest absolute mass is a source of the uncertainty in the determination of the rate of neutrinoless double beta decay[5]}, [6]}, [7]}, [8]}, [9]}.
Actuality, there are models that allow for the lightest neutrino to be massless[10]}.
For those models, the neutrinoless double beta decay rate becomes more predictive since the non-zero masses are directly obtained from the mass squared differences and only a single Majorana phase is allowed.
In cosmology, the absolute neutrino masses are important to early universe phenomena such as big-bang nucleosynthesis, and large scale structure formation[11]}.
And we have previously discussed the role of the absolute masses for neutrinos in the time evolution of lepton number[12]}, [13]}.
Thus, understanding the absolute masses of neutrinos is important for neutrinoless double beta decay, cosmology, and the time evolution of lepton number.
The main goal of this paper is to study a massive neutrino models' stability, with the lightest neutrino being massless, including 1-loop quantum corrections.
